GEOMETRY: Chapter 10 10.4: Other Relationships in Circles.

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Presentation transcript:

GEOMETRY: Chapter : Other Relationships in Circles

Image taken from: Geometry. McDougal Littell: Boston, P Theorem If a tangent and a chord intersect at a point on a circle, then the measure of each angle formed is one half the measure of its intercepted arc.

Ex.1: Line m is tangent to the circle. Find x or y. Answer: a. 114; b. 236 Image taken from: Geometry. McDougal Littell: Boston, P. 681.

Intersecting Lines and Circles If two lines intersect a circle, there are three places where the lines can intersect.

Image taken from: Geometry. McDougal Littell: Boston, P Theorem 10.13: Angles Inside the Circle Theorem If two chords intersect inside a circle, then the measure of each angle is one half the sum of the measures of the arcs intercepted by the angle and its vertical angle.

Image taken from: Geometry. McDougal Littell: Boston, P Theorem Angles Outside the Circle Theorem If a tangent and a secant, two tangents, or two secants intersect outside a circle, then the measure of the angle formed is one half the difference of the measures of the intercepted arcs.

Ex. 2: Find the value of x. Answer: 76 Image taken from: Geometry. McDougal Littell: Boston, P. 681.

Ex. 3: Find the value of x. Answer: 18 Images taken from: Geometry. McDougal Littell: Boston, P.682.

Ex. 4: The Space Shuttle typically orbits at a height of 600 kilometers. Suppose an astronaut takes a picture from point S. What is the measure of arc RQ? Answer: 48 o Images taken from: Geometry. McDougal Littell: Boston, P.682.

10.4, p. 624, #5-28 all